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AFLR2C Example Cases

Data files for several AFLR2C sample cases are provided. Package archives with all of the example cases are provided in aflr2c-examples.tar.gz (tar-gzip archive for Linux/MacOSX) and aflr2c-examples.zip (zip archive for Windows). Copy the package archive files and unpackage them in a location of your choosing to run the example cases. All cases require minimal resources. The input surface edge grid files provided for the sample cases are ASCII formatted files of either BEDGE type or 2D FGRID type. In the following case examples the output mesh file is a big-endian double precision C-binary (.b8) 2D UGRID type file. Alternative file types can be used. By default the output volume mesh is a big-endian double precision C-binary (.b8) 2D UGRID type file named case_name.b8.ugrid. An isotropic element planar mesh can be generated for any of the sample cases using the following command.

aflr2c -i case_name

See the AFLR2C documentation for information on available options and usage. Alternatively you can view text-based documentation at the command line with the following command.

aflr2c -help The XPLT2 program is provided to visualize the mesh that is output from AFLR2C. To display the output mesh using XPLT2 use the following command.

xplt2 case_name.b8.ugrid

Text-based documentation is available at the command line with the following command.

xplt2 -help

Several AFLR2C example cases are provided and described below.

Mesh between two circles

aflr2c -i circle

circle_v1.grid001.png

Quad/tria mesh between two circles

aflr2c -quad -i circle

circle_v2.grid001.png

Mesh in a box

aflr2c -i box

box_v1.grid001.png

Quad/tria mesh in a box

aflr2c -quad box

box_v2.grid001.png

Mesh around NACA0012 airfoil

aflr2c -i n12

n12_v1.grid001.png
n12_v1.grid002.png

Quad/tria mesh around NACA0012 airfoil

aflr2c -quad -i n12

n12_v2.grid001.png
n12_v2.grid002.png

Mesh about a multi-element airfoil

aflr2c -i m3

m3_v1.grid001.png
m3_v1.grid002.png

Quad/tria mesh about a multi-element airfoil

aflr2c -quad -i m3

m3_v2.grid001.png
m3_v2.grid002.png

Mesh with multiple different inner and outer shapes

aflr2c -i shapes.fgrid

shapes_v1.grid001.png

Quad/tria mesh with multiple different inner and outer shapes

aflr2c -quad -i shapes.fgrid

shapes_v2.grid001.png

Mesh for Atlantic ocean with field growth

aflr2c -grow1 -i atlantic

atlantic_v1.grid001.png

Quad/tria mesh for Atlantic ocean with field growth

aflr2c -grow1 -quad -i atlantic

atlantic_v2.grid001.png

Quad/tria mesh for multiple objects with a quad interior core mesh

aflr2c -i things_ic_bnd -ice -o things_ic.b8.ugrid

things_1.png
things_2.png
things_3.png

Quad/tria mesh around NACA0012 airfoil with a quad interior core mesh

aflr2c -i n12 -ice -o n12_v3.b8.ugrid

xn12_0.png
xn12_1.png
xn12_2.png

Quad/tria mesh around multi-element airfoil with a quad interior core mesh

aflr2c -i m3 -ice -o m3_v3.b8.ugrid

xm3_0.png
xm3_1.png
xm3_2.png

Mesh Sizing

In default mode AFLR2C determines element sizing based on interpolation between boundary points (and source points, if any). As mesh generation advances the sizing is propagated by continued interpolation locally. Alternatively, an external sizing function can be coded and linked with the executable. A built-in external sizing function is provided for testing and example. By itself it is not useful for practical problems. However, developers can integrate specialized sizing functions within the AFLR2C executable. The built-in function simply creates a continuous field that varies radially from the center of the domain outward to the boundaries. At the center the sizing is smaller than specified at the boundaries. Another alternative for sizing is to use a background mesh and function file for interpolation. If the files case_name.back.b8.ugrid and case_name.back.sfunc exist then it is assumed that use of a background mesh is desired. Note that any supported and readable mesh and function file format and type are equally as acceptable as .b8.ugrid and .sfunc. The case name case_name must be the same as the input surface mesh file. The option flag -no_back can be added to ignore these files.

Box with external isotropic sizing function

The following example uses the built-in external sizing function. If an alternative routine is created then use of that function can be controlled in the same manner or by using the correct meval=# for the alternative function. The provided built-in sizing function has test cases for meval=1,2,...6 (4,5,6 require use of a metric - see next section). This case also creates a background grid sizing field that will be used in the next case. The option flag meval=1 activates use of the alternative built-in external sizing function #1 and the flag mwbgfunc=1 (not required for normal usage) simply creates an output function file box.back.sfunc which contains the isotropic sizing for each mesh vertex.

aflr2c -i box meval=1 mwbgfunc=1

box_v3.grid001.png

Box with background mesh for interpolation of isotropic sizing

Another alternative for sizing is to use a background mesh and function file for interpolation. If the files box.back.b8.ugrid and box.back.sfunc exist then it is assumed that use of a background mesh is desired. Note that any supported and readable mesh and function file format and type are equally as acceptable as .b8.ugrid and .sfunc. The option flag -no_back can be added to ignore these files. In this test case the background mesh sizing field is derived from the previous case. It could also be generated from another code that bases the sizing on the computed physics or other criteria. The resulting mesh is equivalent to the previous case (on which it is based). However, it does differ since here we are interpolating rather than determining the sizing analytically.

cp box.b8.ugrid box.back.b8.ugrid
aflr2c -i box

Anisotropic Adaptation/Generation

In default mode AFLR2C determines element sizing based on interpolation between boundary points (and source points, if any). Alternatively, the sizing can be interpolated from a background mesh. In addition, the background mesh may specify, in a function file, either the isotropic mesh sizing or directional metric based sizing. If the executable is able to find a set of files named case_name.back.* for the background mesh that is a valid mesh type file along with a background sizing function file that is a valid function file then the background data will be read in and used. The case name case_name must be the same as the input surface mesh file. The option flag -no_back can be added to ignore these files. If the metric option is on (mmet=1 or 2) then the function file must contain a metric for every background mesh vertex. And, if the metric option is off (mmet=0) as it is by default then the function file must contain an isotropic spacing for every background mesh vertex. With a background mesh all element sizing is interpolated from the background mesh.

The first step in the mesh generation process in adaptation mode is a regeneration of the input boundary edge grid. The vertex spacing on the boundary edges is determined from the background mesh. Cubic splines based upon the input boundary edge grid are used for geometric specification. As such, the input boundary edge grid should be of sufficient resolution to resolve the geometry. Splines are split between boundary edges of different IDs and at discontinuities. The detection of discontinuities is controlled by the input parameter angdbe (discontinuous boundary edge angle). If the angle between two adjacent boundary edge vectors differ by more than angdbe then the location is considered discontinuous. The discontinuity angle may need to be modified for configurations that do not have differing boundary edge IDs and low-angle discontinuities.

Subsequent mesh generation steps follow the normal process, except that sizing is interpolated from the background mesh. With metric based adaptation/generation it is recommended that right angle elements be used (mpp=3) as the point placement strategy uses alignment with the background metric. Typically the only option required is -met3 (mmet=1 mpp=3). Note that at present smoothing is turned off when metrics are used.

Box with a cross

The following example uses the built-in external sizing function and creates the metric field instead of using a background mesh. If an alternative routine is created then use of that function can be controlled in the same manner or by using the correct meval=# for the alternative function. The provided built-in sizing function has test cases for meval=1,2,...6 (4,5,6 require use of a metric - see next section). The option flag met3 turns on use of the metric and right angle point placement and the option flag meval=5 activates use of the alternative built-in external sizing function #3 (blended cross).

aflr2c -i cross -met3 meval=5

cross.grid001.png

Supersonic NACA Airfoil

The following example for a NACA airfoil in a supersonic flow field uses a supplied background mesh and metric field. The option flag met3 turns on use of the metric and right angle point placement.

aflr2c -i naca -met3

naca.grid001.png

Scramjet

The following example for a scramjet field uses a supplied background mesh and metric field. The option flag met3 turns on use of the metric and right angle point placement.

aflr2c -i scramjet -met3

scramjet.grid001.png

Shock Bubble Interaction

The following example for a shock interacting with bubble in a supersonic flow field uses a supplied background mesh and metric field. The option flag met3 turns on use of the metric and right angle point placement.

shock_bubble.grid001.png

The BSURF2 program is also provided to generate boundary edge grid files

It is an interactive program and the prompts should be descriptive enough to allow usage. Package archives with example files for the BSURF2 code are provided in bsurf2-examples.tar.gz (tar-gzip archive for Linux/MacOSX) and bsurf2-examples.zip (zip archive for Windows).BSURF2  is not that well documented and it would be much easier to use in a GUI. However it gets the job done and is not that painful to use. The objects in the geometry can be a circle, polygon, or come from a data file. The data file must be a string of x and y coordinates (one set per line) in sequential order that form a closed curve (do not duplicate the last data point). The direction (clockwise or not) is not important. A spline is generated for each object and automatically split at the first and last data points and at detected discontinuities. Spline split points can be added or deleted. A script file is created that allows one to rerun a case with a corrected error or slightly different parameters. Edit the script file (default name is bsurf2.script) to make changes and rerun BSURF2. The # comments should provide information necessary to modify the right parameters. If you make an error while running BSURF2 and want to start over from a previous point in the session then kill the process. In this case edit the script file by deleting everything from the point you made the unwanted step to the end of the file. Then rerun BSURF2 using the script file you edited as the input script file. The program will redo all the steps contained in the script file and return standard input control to you when it reaches the end of the file. To run BSURF2 in interactive mode simply enter the following and follow the interactive prompts.

bsurf2

Note that BSURF2 generates ASCII formatted type BEDGE edge grid files. These are exactly the same as the older, and now obsolete, BSURF type files that older versions of BSURF2 generated. AFLR2C can input BEDGE, BSURF, 2D FGRID or 2D UGRID file types. See the UG_IO documentation for a description of standard UG_IO file types used by AFLR2C.

BSURF2 example cases are provided and described below. The script files for each are configured to generate a suitable boundary edge grid for AFLR2C.

Mesh around NACA0012 airfoil

bsurf2 n12

aflr2c -i n12

Mesh with multiple different inner and outer shapes

bsurf2 shapes

aflr2c -i shapes